On the Stability of the Finite Difference based Lattice Boltzmann Method
KAUST DepartmentPhysical Sciences and Engineering (PSE) Division
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AbstractThis paper is devoted to determining the stability conditions for the finite difference based lattice Boltzmann method (FDLBM). In the current scheme, the 9-bit two-dimensional (D2Q9) model is used and the collision term of the Bhatnagar- Gross-Krook (BGK) is treated implicitly. The implicitness of the numerical scheme is removed by introducing a new distribution function different from that being used. Therefore, a new explicit finite-difference lattice Boltzmann method is obtained. Stability analysis of the resulted explicit scheme is done using Fourier expansion. Then, stability conditions in terms of time and spatial steps, relaxation time and explicitly-implicitly parameter are determined by calculating the eigenvalues of the given difference system. The determined conditions give the ranges of the parameters that have stable solutions.
CitationOn the Stability of the Finite Difference based Lattice Boltzmann Method 2013, 18:2101 Procedia Computer Science
JournalProcedia Computer Science
Conference/Event name13th Annual International Conference on Computational Science, ICCS 2013